SOSTOOLS Version 4.00 Sum of Squares Optimization Toolbox for MATLAB
SOSTOOLS Version 4.00 Sum of Squares Optimization Toolbox for MATLAB
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发表时间：
2013-10
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通讯作者：
A. Papachristodoulou;James Anderson;G. Valmórbida;S. Prajna;Peter J Seiler;P. Parrilo;M. Peet;Declan S. Jagt
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作者：
A. Papachristodoulou;James Anderson;G. Valmórbida;S. Prajna;Peter J Seiler;P. Parrilo;M. Peet;Declan S. Jagt
SOSTOOLS v4.00的发布正值2002年4月SOSTOOLS v1.00最初发布20周年之际。SOSTOOLS最初被设想为一种灵活的工具，用于解析和解决多项式优化问题，使用多项式正性约束的SOS紧致，并能够适应SOS不断发展的应用基础。除了SOSTOOLS之外，现在还有各种SOS编程解析器，包括YALMIP、Gloptipoly、SumOfSquares等。我们希望SOSTOOLS仍然是SOS编程的最直观、最健壮和最具适应性的工具箱。半定规划的最新进展为解决大平方和规划问题开辟了新的可能，我们希望在接下来的十年里，SOS方法将在不同的领域得到广泛的应用。在SOSTOOLS v4.00中，我们实现了一种解析方法，它将解析器的计算和内存需求降低到低于SDP解算器本身的水平。我们重新开发了多项式决策变量的内部结构。具体地说，使用sossosvar、sosPolyvar、sosmatrixvar等进行的多项式和SOS变量声明现在返回新的多项式结构dpvar。这种新的多项式结构记录在随附的dpvar指南中，并将SOS程序中的标量SDP决策变量与用于构建SOS程序的自变量分离。因此，解析器的复杂性几乎与决策变量的数量成线性关系。这些变化的结果是，几乎所有用户都会注意到速度的显著提高，其中大规模问题的加速效果最为显著。解析时间现在始终不到SDP解算器所用时间的10%。最后，SOSTOOLS现在支持MOSEK求解器接口以及SeDuMi、SDPT3、CSDP、SDPNAL、SDPNAL+和SDPA求解器。
The release of SOSTOOLS v4.00 comes as we approach the 20th anniversary of the original release of SOSTOOLS v1.00 back in April, 2002. SOSTOOLS was originally envisioned as a flexible tool for parsing and solving polynomial optimization problems, using the SOS tightening of polynomial positivity constraints, and capable of adapting to the ever-evolving fauna of applications of SOS. There are now a variety of SOS programming parsers beyond SOSTOOLS, including YALMIP, Gloptipoly, SumOfSquares, and others. We hope SOSTOOLS remains the most intuitive, robust and adaptable toolbox for SOS programming. Recent progress in Semidefinite programming has opened up new possibilities for solving large Sum of Squares programming problems, and we hope the next decade will be one where SOS methods will find wide application in different areas. In SOSTOOLS v4.00, we implement a parsing approach that reduces the computational and memory requirements of the parser below that of the SDP solver itself. We have re-developed the internal structure of our polynomial decision variables. Specifically, polynomial and SOS variable declarations made using sossosvar, sospolyvar, sosmatrixvar, etc now return a new polynomial structure, dpvar. This new polynomial structure, is documented in the enclosed dpvar guide, and isolates the scalar SDP decision variables in the SOS program from the independent variables used to construct the SOS program. As a result, the complexity of the parser scales almost linearly in the number of decision variables. As a result of these changes, almost all users will notice a significant increase in speed, with large-scaleproblems experiencing the most dramatic speedups. Parsing time is now always less than 10% of time spent in the SDP solver. Finally, SOSTOOLS now provides support for the MOSEK solver interface as well as the SeDuMi, SDPT3, CSDP, SDPNAL, SDPNAL+, and SDPA solvers.